Mechanics

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Mechanics
W Richards The Weald School
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Uncertainty
Consider a ruler
It has an uncertainty of 0.5mm
Now consider the time taken for a ball to drop
Drop no. Drop 1 Drop 2 Drop 3 Uncertainty
Time taken to fall/s
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Summary
Take appropriate measurements and complete the
table
Thing to measure What device? Meas. 1 Meas. 2 Meas. 3 Ave. Uncert-ainty uncert-ainty
Width of book
Width of table leg
Diam. of hair
Depth of beaker
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Density

1. What is the density of a piece of wood of volume
   2m3 and mass 1200kg?
2. Air only has a density of 1.3kg/m3. What is the
   mass of 0.2m3 of air?
3. Carbon dioxide is more dense and the same volume
   would have a mass of 0.38kg. What is its
   density?
4. The mercury in a thermometer has a volume of
   5x10-5m3. If the density of the mercury is
   13600kg/m3 what mass of mercury is in the
   thermometer?

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Density
Object Mass/kg Volume/m3 Density/ kg/m3



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Standard Form and prefixes
Prefix Symbol Multiplier
Giga G 109
Mega M 106
Kilo K 103
Milli m 10-3
Micro µ 10-6
Nano n 10-9
Pico p 10-12

• Try these hard questions
• What is 1mm2 in m2?
• What is 1µm2 in m2?
• What is 10mm3 in m3?
• How many pm3 fit in a cubic kilometre?

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International System of Units
There are six basic quantities we need to know
about. Their units are called S.I. units
Base quantity Base unit Symbol
Length metre m
Mass kilogram kg
Time second s
Current ampere A
Temperature Kelvin K
Amount of substance mole mol
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Derived Units
Derived units are units that are made up out of
base units. For example, the unit for speed
(metre per second) comes from the base units for
distance and time.
The following units are derived. Use suitable
equations to express each unit in terms of base
units

1. Newton (force)
2. Joule (energy)
3. Pascal (pressure)
4. Watt (power)
5. Coulomb (electric charge)

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Homogeneity
It doesnt make sense! You cant add kilograms
to metres. Thats just silly.
Calculate the following
10kg 5m ??
For an equation to be correct it has to be
homogenous. In other words, it has to add and
equal the same type of units.
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Distance, Speed and Time revision

1. Simon walks 200 metres in 40 seconds. What is
   his speed?
2. Howard covers 2km in 1,000 seconds. What is his
   speed?
3. How long would it take Ryan to run 100 metres if
   he could run at 12m/s?
4. Ben throws a book at Dan and it travels at 50m/s
   for 0.2s. How far away was Dan?
5. Chris is learning to drive. He drives his car at
   85mph (about 40m/s). How long does it take him
   to drive 20km?

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Some subtle differences
Distance is how far you have gone,
displacement is how far you are and can be
positive or negative
Distance Displacement
Distance Displacement
Distance Displacement
Distance Displacement
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Some subtle differences
Distance is how far you have gone,
displacement is how far you are and can be
positive or negative
Speed Velocity
Speed Velocity
Speed Velocity
Speed Velocity
Speed is how fast you go. Velocity is how
fast in a given direction.
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Vector vs. scalar
Scalar quantities have size only and no
direction. Vector quantities have both size and
direction.
Scalar or vector???
Scalar
Vector
8. Power
2. Distance
12. Acceleration
1. Mass
6. Energy
7. Time
3. Displacement
4. Speed
10. Current
11. Force
5. Velocity
9. Momentum
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40 30 20 10 0




Distance (metres)
Time/s
20 40 60 80 100

1. What is the velocity during the first 20 seconds?
2. What is the displacement after 60 seconds?
3. What is the velocity during the last 40 seconds?
4. What is the displacement after 100 seconds?

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20 10 0 -10 -20




Displacement (metres)
Time/s
20 40 60 80 100

1. What was the displacement after 20 seconds?
2. What was the velocity between 20 and 40 seconds?
3. When was this person travelling the fastest?
4. What was the average speed for the first 40
   seconds?

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Understanding Velocity
1) Is this car travelling at constant speed? 2)
Is this car travelling at constant velocity?
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Understanding Velocity
40 30 20 10 0




Displacement (metres)
Time/s
20 40 60 80 100

1. Whats the average velocity?
2. Whats the velocity at 60s?

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Acceleration

1. Ryan accelerates on his bike from 0 to 10ms-1 in
   5 seconds. What is his acceleration?
2. Harry drops a ball and it accelerates downwards
   at a rate of 10ms-2 for 12 seconds. What speed
   did it reach?
3. A car accelerates from 10 to 20ms-1 with an
   acceleration of 2ms-2. How long did this take?
4. A rocket accelerates from 1,000ms-1 at a rate of
   20ms-2 for 2 minutes. What speed did it reach?

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80 60 40 20 0




Velocity m/s
T/s
10 20 30 40 50

1. How fast was the object going after 10 seconds?
2. What is the acceleration from 20 to 30 seconds?
3. What was the acceleration from 30 to 50s?
4. How far did the object travel altogether?

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20 10 0 -10 -20




Velocity (metres)
Time/s
20 40 60 80 100

1. When did the object have zero acceleration?
2. What is the average acceleration from 0 to 40s?
3. What was the acceleration from 40 to 60s?
4. How far did the object go between 50 and 100s?

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A closer look at motion graphs
Consider a bouncing ball
Displacement
Time
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A closer look at motion graphs
Consider a bouncing ball
Velocity
Time
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A closer look at motion graphs
Consider a bouncing ball
Acceleration
Time
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Equations of Motion
If were talking about any object travelling in a
straight line with constant acceleration then we
can use these 4 golden equations
v
u
Ave. velocity (u v) / 2
Acc (v u) / t
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Equations of Motion
From eqn 2 t (v-u) / a
v
From eqn 1 x t(uv) / 2
t(v-u)/2
u
ut
From equation 2 (v-u) at
2ax v2 u2
Therefore x ut t/2 x at
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Equations of Motion
u v
x
t
2
v
u at
Theyre golden!
x ut ½at2
v2 u2 2ax
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Example questions

1. Ben drops a ball on Dans foot. How long does
   the ball take to fall 1m? 2m? Why is the second
   answer not twice the first?
2. Ryan flies to Belgium. His aeroplane has a
   maximum acceleration on the ground of 3.4ms-2.
   What is the minimum length of runway needed to
   reach its take off speed of 110ms-1 and how long
   will this take?
3. Luke likes watching kangaroos. A kangaroo jumps
   to a vertical height of 2.8m. For how long was
   it in the air?
4. Tom likes baseball. A baseball pitcher can
   release a ball at 40ms-1 after accelerating
   through a distance of 2.5m. Calculate the
   average acceleration of the ball.

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Example questions

1. Andrew wants to play with the air track. The air
   track is slightly tilted. He pushes a trolley up
   the track with a speed of 1ms-1 and its
   acceleration due to the tilt is 0.5ms-2 down the
   track. How long does it take to drop 1m below
   the starting point?
2. Howard travels in a rocket powered sledge and
   accelerates from rest to 284ms-1 in 5s and then
   comes to a rest in 1.5s. Calculate his
   acceleration in both stages.
3. Harry has a good chance of surviving a car crash
   with a seatbelt on if his deceleration does not
   exceed 30g. Calculate the distance by which the
   front end of the car must collapse in if a crash
   occurs at 70mph.

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Vertical Projection
If I throw this ball upwards with a speed of
40ms-1 how high will it go?
Use v2 u2 2ax
0 402 (2 x -9.81 x x)
0 1600 19.62x
1600 19.62x
x 1600/19.62
x 81.5m
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Practice Questions

1. How far will a cricket ball go if it is thrown
   upwards with an initial velocity of 10ms-1?
2. How far will a table tennis ball go if it is
   thrown upwards with an initial velocity of 5ms-1?
3. A human cannonball is projected vertically
   upwards and she reaches a vertical height of 20m
   before coming back down. How fast was she going
   when she left the cannon?
4. A test tube falls off the table. If the table is
   1m high how fast was the test tube going when it
   hit the floor?

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Measuring g
Consider the equation x ut ½at2
If we consider a ball being dropped then u0, so
x ½at2
We also know that a g, therefore
x ½gt2
x ½ g t2
y m x c
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Projectile Motion
Aha! If I let go of the branch when he fires his
gun Ill be safe because the bullet will go above
me
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Projectile Motion
Question how long did this take and how fast
was the bullet?

1. Use x ut ½at2 vertically to find the time
2. Then use speed distance / time horizontally to
   get the speed

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Example questions

1. Ben throws a bowling ball at Tom and it lands on
   his foot. If the ball started 1.2m above Toms
   foot and the distance between them was 2m
   calculate both the time taken and the initial
   velocity of the ball.
2. Rob fires a gun and the bullet leaves the barrel
   at a speed of 200ms-1. If it landed on the
   ground 500m away calculate how long the journey
   took and how high up Rob was holding the gun from
   ground level.
3. Andrew likes knocking test tubes off the table.
   If he hits one with an initial velocity of 2ms-1
   and the table is 1m high calculate the time taken
   for the test tube to hit the floor and how far
   away from the table it landed.

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Recap questions

1. Andrew Murray hits a tennis ball and it passes
   horizontally over the net and lands just inside
   the baseline of the court. The net has a height
   of 1.07m and is 11.9m from the baseline. Find
   the horizontal speed of the ball.
2. David Beckham takes a free kick and it flies into
   the top corner horizontally. If the corner is
   2.4m above the ground and the goal is 18m away
   calculate the time taken for the ball to reach
   the goal.

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Newtons 1st Law of Motion
Basically, a body will remain at rest or continue
to move with constant velocity as long as the
forces acting on it are balanced.
and an unbalanced backwards force will make me
slow down
An unbalanced forwards force will make me
accelerate
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Newtons 2nd Law of Motion
The acceleration of a body is proportional to the
resultant force causing its acceleration and is
in the same direction.
In other words force mass x acceleration
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Revision questions

1. A force of 1000N is applied to push a mass of
   500kg. How quickly does it accelerate?
2. A force of 3000N acts on a car to make it
   accelerate by 1.5ms-2. How heavy is the car?
3. A car accelerates at a rate of 5ms-2. If it
   weighs 500kg how much driving force is the engine
   applying?
4. A force of 10N is applied by a boy while lifting
   a 20kg mass. How much does it accelerate by?

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Testing Newtons 2nd Law
For each version of the experiment

1. Draw a diagram of how you set it up
2. Describe your method
3. Describe what equipment you used to get the
   results and how you analysed them (you only need
   to do this once as theyre both the same).

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Newtons 3rd Law of Motion
When body A exerts a force on body B, body B
exerts an equal and opposite force on body A.
My third law says that if I push to the right I
will move backwards as well.
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Newtons 3rd Law of Motion
What will happen if I push this satellite away
from me?
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Types of Forces
Electromagnetic/electrostatic
Gravitational (Wmg)
Nuclear (2 types)
Describe each force, including a comment on the
distance it works over, whether it repels or
attracts and other important points
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Free body force diagrams
The Earth pulls Newton down with a gravitational
force of 700N.
Newton pulls the Earth up with a gravitational
force of 700N.
This is a Newton III pair of forces
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Free body force diagrams 2
Consider a man standing on a table on the Earth
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Newton I vs. Newton III
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Summary
Newton I Newton III
A law about the forces on _ _____ ____ A law about the forces on ____ _______ _____
Concerns any _____ of forces Always concerns ____ forces only
The forces can be ______ types Both forces are ___ ______ type
If there are two forces and the body is in equilibrium the forces are _____ and ________ The two forces are ALWAYS ______ and ________
Newton I only applies when the body is in ________ Newton III ______ applies
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Random recap questions

1. Nick runs the last 100m of a 200m race over 15s.
   If he was accelerating at a rate of 1ms-2 during
   those 15s how fast was he running when he passed
   the 100m mark?
2. Ben throws a ball from the 1st floor at Ryan
   below. If the ball travels for 1.5s before
   hitting Ryan how far above Ryan is Ben? If Ryan
   is 20m away from the building how fast did Ben
   throw it?
3. Dan is swinging a conker around on a piece of
   string. Draw a free body force diagram for each
   object (you may find it easier to draw both on
   the same diagram).
4. For each of the forces in the previous two
   diagrams identify the Newton III pair and
   describe what the force is, what is acts on and
   its direction.

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Vectors
14.1km
100.1ms-1
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Resolving Vectors
Consider a diagonal push
This force is given by F1 F sin ?
This force is given by F2 F cos ?
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Resolving Vectors example questions
Calculate the horizontal and vertical components
of the following
1)
2)
10N
20N
35O
50O
Work out the size and direction of the resultant
force
3)
4)
20N
8N
15N
10N
50O
45O
30O
80O
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Free body force diagrams 3
Consider a man on a sloping table
Reaction (a contact force) is perpendicular to
the surface. Friction (a tangential contact
force) goes up the slope. Lets combine the
forces
Resultant force is zero, so no acceleration
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Free body force diagrams
1) Draw a free body force diagram for a ladder
against a wall.
2) A car pulls a caravan along the M25. Draw a
free body force diagram for the caravan.
4) Draw a free body force diagram for a 2-wheel
drive (engine at the front) car driving up the M1
as well.
3) Draw a free body force diagram for a 4-wheel
drive car driving up the M1.
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Moments revision
A moment is a turning force, e.g. trying to
open or close a door or using a spanner. The
size of the moment is given by
Moment (in Nm) force (in N) x PERPENDICULAR
distance from pivot (in m)
Calculate the following turning moments
5 metres
100 Newtons
2 metres
200 Newtons
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Turning Moments revision
The anti-clockwise moment is bigger so the seesaw
will turn anti-clockwise
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Balanced or unbalanced?
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Turning Moments
Consider a man walking along a plank of wood on a
cliff.
How far can he walk over the cliff before the
plank tips over?
Aaarrgghh
Mans weight 800N
Planks weight 200N
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Another example
Consider a car on a suspension bridge
How much weight does each support take?
20m
Weight of car 10,000N
Weight of bridge 500,000N
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A recap question
1) State the principle of moments
2) Calculate the mass of man in the example
given below
30kg
1.2m
0.4m
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Momentum
Any object that has both mass and velocity has
MOMENTUM. Momentum (symbol p) is simply given
by the formula

• What is the momentum of the following?
• A 1kg football travelling at 10ms-1
• A 1000kg Ford Capri travelling at 30ms-1
• A 20g pen being thrown across the room at 5ms-1
• A 70kg bungi-jumper falling at 40ms-1

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Conservation of Momentum
In any collision or explosion momentum is
conserved (provided that there are no external
forces have an effect). Example question
Two cars are racing around the M25. Car A
collides with the back of car B and the cars
stick together. What speed do they move at after
the collision?
Mass 1000kg
Mass 800kg
Mass 1800kg
Momentum before momentum after so 1000 x
50 800 x 20 1800 x V V
36.7ms-1
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Momentum in different directions
What happens if the bodies are moving in opposite
directions?
Momentum is a VECTOR quantity, so the momentum of
the second car is negative
Total momentum 1000 x 50 800 x 20 34000
kgms-1
Speed after collision 34000 kgms-1 / 1800
18.9ms-1
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Another example
Consider the nuclear decay of Americium-241
If the new neptunium atom moves away at a speed
of 5x105 ms-1 what was the speed of the alpha
particle?
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More questions

1. A white snooker ball moving at 5m/s strikes a red
   ball and pots it. Both balls have a mass of 1kg.
   If the white ball continued in the same
   direction at 2m/s what was the velocity of the
   red ball?
2. A car of mass 1000kg heading up the M1 at 50m/s
   collides with a stationary truck of mass 8000kg
   and sticks to it. What velocity does the
   wreckage move forward at?
3. A defender running away from a goalkeeper at 5m/s
   is hit in the back of his head by the goal kick.
   The ball stops dead and the players speed
   increases to 5.5m/s. If the ball had a mass of
   500g and the player had a mass of 70kg how fast
   was the ball moving?
4. A gun has a recoil speed of 2m/s when firing. If
   the gun has a mass of 2kg and the bullet has a
   mass of 10g what speed does the bullet come out
   at?

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Newtons 2nd Law and Impulse
Instead of Fma Newton actually said that the
force acting on an object is that objects rate
of change of momentum. In other words

• For example, David Beckham takes a free kick by
  kicking a stationary football with a force of
  40N. If the ball has a mass of 0.5kg and his
  foot is in contact with the ball for 0.1s
  calculate
• The change in momentum of the ball (its impulse),
• The speed the ball moves away with

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Example questions

1. Ben likes playing golf. He strikes a golf ball
   with a force of 80N. If the ball has a mass of
   200g and the club is in contact with it for 0.2s
   calculate a) the change in momentum of the golf
   ball, b) its speed.
2. Nick thinks its funny to hit tennis balls at
   Tom. He strikes a serve with a force of 30N. If
   the ball has a mass of 250g and the racket is in
   contact with it for 0.15s calculate the balls
   change in momentum and its speed.
3. Dan takes a dropkick by kicking a 0.4kg rugby
   ball away at 10m/s. If his foot was in contact
   with the ball for 0.1 seconds calculate the force
   he applied to the ball.
4. Simon strikes a 200g golf ball away at 50m/s. If
   he applied a force of 50N calculate how long his
   club was in contact with the ball for.

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Another way to ask the same question
Heres a situation we looked at earlier
Whats the impulse of the car on the left if the
cars stick together?
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Energy loss in collisions
In the Forces module we looked at how to
calculate an objects kinetic energy
Kinetic energy ½ x mass x velocity squared in J
in kg in m/s
Weve also said that in a collision momentum is
conserved (unless an external force acts). The
same cannot usually be said for kinetic energy
For example, consider the following collision.
How much kinetic energy is lost?
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Energy loss in collisions
Consider a head-on collision where the cars stick
together. How much kinetic energy is lost in
this example? Where does all the energy go?
Before
After
In this example more kinetic energy was lost. We
say it was a less elastic collision. An
elastic collision is one where the kinetic
energy is conserved.
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Work done
Work done (in joules) is simply the force needed
to move an object multiplied by the distance
moved in the direction of the force
?W F?x
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Power
Power (in watts) is the rate of doing work
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Random questions on work and power

1. Luke pushes Ben in the direction of a cliff. If
   he uses a force of 40N and he moves Ben 10m in 4s
   calculate the work done and Lukes power rating.
2. Dan runs up some stairs and has a power rating of
   600W while he does so. If he does it in 5
   seconds and his weight is 750N calculate how high
   the stairs are.
3. A man pulls a block of wood at an angle of 200 to
   the horizontal and uses a force of 50N. If the
   distance travelled horizontally is 5m calculate
   the work done by the man and his power if the
   journey lasted 10 seconds.

50N
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Conservation of Energy
Consider a bouncing ball
Gravitational Potential Energy
Time
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Conservation of Energy
Consider a bouncing ball
Kinetic Energy
Time
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Conservation of Energy
Now put these graphs together
Kinetic Energy
Total energy of the ball
Time
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Radioactivity
W Richards The Weald School
76
Structure of the atom
A hundred years ago people thought that the atom
looked like a plum pudding a sphere of
positive charge with negatively charged electrons
spread through it
Ernest Rutherford, British scientist
I did an experiment (with my colleagues Geiger
and Marsden) that proved this idea was wrong. I
called it the Scattering Experiment
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The Rutherford Scattering Experiment
Alpha particles (positive charge, part of helium
atom)
Thin gold foil
Most particles passed through, 1/8000 were
deflected by more than 900
Conclusion atom is made up of a small,
positively charged nucleus surrounded by
electrons orbiting in a cloud.
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The structure of the atom
Atoms are roughly 10-10m in diameter, while the
nucleus is 10-15 10-14m
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The structure of the atom
Particle Relative Mass Relative Charge
Proton 1u (1.7x10-27kg) 1.6x10-19C
Neutron 1u (1.7x10-27kg) 0
Electron 0 -1.6x10-19C
No. of neutrons N A - Z
80
Isotopes
An isotope is an atom with a different number of
neutrons
A radioisotope is simply an isotope that is
radioactive e.g. carbon 14, which is used in
carbon dating.
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Quarks
We can investigate the structure of protons by
bombarding them with electrons
Low energy scattering
P
e-
Elastic collision. Electrons and protons behave
as expected.
High energy scattering
P
e-
Inelastic collision. Energy is absorbed by the
proton and increases its internal energy. This
is Deep Inelastic Scattering and suggests that
the proton is made of smaller particles called
quarks.
82
Introduction to Radioactivity
Some substances are classed as radioactive
this means that they are unstable and
continuously give out radiation
Radiation
The nucleus is more stable after emitting some
radiation this is called radioactive decay.
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Ionisation
Radiation is dangerous because it ionises atoms
in other words, it turns them into ions by
giving them enough energy to knock off
electrons
Alpha radiation is the most ionising (although
short range). Ionisation causes cells in living
tissue to mutate, usually causing cancer.
84
The Geiger-Muller Tube
85
Types of radiation
1) Alpha (?) an atom decays into a new atom
and emits an alpha particle (2 protons and 2
______ the nucleus of a ______ atom)
Unstable nucleus
New nucleus
Alpha particle
2) Beta (?) an atom decays into a new atom by
changing a neutron into a _______ and electron.
The fast moving, high energy electron is called a
_____ particle.
Beta particle
Unstable nucleus
3) Gamma after ? or ? decay surplus ______ is
sometimes emitted. This is called gamma
radiation and has a very high ______ with short
wavelength. The atom is not changed.
Words frequency, proton, energy, neutrons,
helium, beta
Unstable nucleus
New nucleus
Gamma radiation
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Changes in Mass and Proton Number
Alpha decay
Beta - decay
Beta decay
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Blocking Radiation
Each type of radiation can be blocked by
different materials
Sheet of paper (or 6cm of air will do)
Few mm of aluminium
Few cm of lead
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Summary
Property Alpha Beta - Beta Gamma
Charge
Rest mass
Penetration
What is it?
Ionising ability
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Deflection by Magnetic Fields
2 protons, 2 neutrons, therefore charge 2
Alpha and beta particles have a charge
1 electron, therefore charge -1
-
Because of this charge, they will be deflected by
electric and magnetic fields
-
90
Background Radiation
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Nuclear fission
New nuclei (e.g. barium and krypton)
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Chain reactions
Each fission reaction releases neutrons that are
used in further reactions.
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Radioactive Decay
Radioactivity is a random process. The number of
radioisotopes that will decay clearly depends on
the number of radioisotopes present at that point
in time
Activity (in Bq) ?N
? The decay constant and has units of s-1.
It is constant for a particular radioisotope.
94
Half Life
The decay of radioisotopes can be used to measure
the materials age. The HALF-LIFE of an atom is
the time taken for HALF of the radioisotopes in a
sample to decay
After 3 half lives another 2 have decayed (14
altogether)
After 2 half lives another half have decayed (12
altogether)
After 1 half life half have decayed (thats 8)
At start there are 16 radioisotopes
95
A radioactive decay graph
Count




Time
96
Half Life
To calculate half life there are a few methods




1) Read from a graph
2) Calculate using an equation
97
Half Life questions

1. The graph shows the activity of a radioisotope.
   Determine the half life and decay constant.
2. If there are 106 atoms present right now
   calculate how many will decay over the next
   second.

100s

1. What percentage of a sample of radioactive
   material will exist after 200 years if the half
   life is 50 years?
2. Uranium decays into lead. The half life of
   uranium is 4,000,000,000 years. A sample of
   radioactive rock contains 7 times as much lead as
   it does uranium. Calculate the age of the sample.